# Hardness of approximating the shortest vector problem in lattices

@article{Khot2004HardnessOA, title={Hardness of approximating the shortest vector problem in lattices}, author={Subhash Khot}, journal={45th Annual IEEE Symposium on Foundations of Computer Science}, year={2004}, pages={126-135} }

Let p > 1 be any fixed real. We show that assuming NP /spl nsube/ RP, it is hard to approximate the shortest vector problem (SVP) in l/sub p/ norm within an arbitrarily large constant factor. Under the stronger assumption NP /spl nsube/ RTIME(2/sup poly(log n)/), we show that the problem is hard to approximate within factor 2/sup log n1/2 - /spl epsi// where n is the dimension of the lattice and /spl epsi/> 0 is an arbitrarily small constant. This greatly improves all previous results in l/sub… Expand

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